Image reconstruction from coded data: II Code design

A strategy is given for the design of coded apertures with respect to a given class of objects that are to be imaged. Previous knowledge of the first- and second-order statistics for the object class is assumed. The object class is characterized by its Karhunen-Loève eigenvectors and eigenvalues, whereas the imaging system is characterized by its singular-value decomposition. We introduce the concept of alignment in which the aperture parameters are adjusted until the system is tuned to measure the given object class well. A mean-square-error figure of merit that indicates degree of alignment is given, and alignment is performed by standard optimization techniques. We illustrate this technique with a simple proof-of-principle experiment. These concepts are general and may be applied to any linear imaging system.